Displaying similar documents to “New sufficient conditions for a center and global phase portraits for polynomial systems.”

Sufficient conditions for the existence of a center in polynomial systems of arbitrary degree.

Hector Giacomini, Malick Ndiaye (1996)

Publicacions Matemàtiques

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In this paper, we consider polynomial systems of the form x' = y + P(x, y), y' = -x + Q(x, y), where P and Q are polynomials of degree n wihout linear part. For the case n = 3, we have found new sufficient conditions for a center at the origin, by proposing a first integral linear in certain coefficient of the system. The resulting first integral is in the general case of Darboux type. By induction, we have been able to generalize these results for polynomial...

Five limit cycles for a simple cubic system.

Noel G. Lloyd, Jane M. Pearson (1997)

Publicacions Matemàtiques

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We resolve the centre-focus problem for a specific class of cubic systems and determine the number of limit cycles which can bifurcate from a fine focus. We also describe the methods which we have developed to investigate these questions in general. These involve extensive use of Computer Algebra; we have chosen to use REDUCE.

Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C.

Colin Christopher, Christiane Rousseau (2001)

Publicacions Matemàtiques

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In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it. ...

A sufficient condition for a polynomial centre to be global

Marco Sabatini (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A sufficient condition is given in order that a centre of a polynomial planar autonomous system be a global centre.

Chordal cubic systems.

Marc Carbonell, Jaume Llibre (1989)

Publicacions Matemàtiques

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We classify the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincaré sphere are isolated and have linear part non-identically zero.